How to create face out of corner?
Set snap to 'Vertex' (target) and 'Active' (..,element, source)
Switch on 'Automatically merge vertices'
In vertex mode, select the two vertices at the ends of one of the inner edges, corner last.
E extrude the edge implied by the two vertices, snapping the corner vertex to the one at the other end of its edge.


It depends, really, this way isn't necessarily faster than yours, but I nearly always have my snap set this way anyway.. and if fiddling, often use the auto-weld. Perhaps the only point is, you don't need to be in Edge mode to extrude the edge.